On plurisubharmonic defining functions for pseudoconvex domains in $\mathbb{C}^2$
Abstract
We investigate the question of existence of plurisubharmonic defining functions for smoothly bounded, pseudoconvex domains in . In particular, we construct a family of simple counterexamples to the existence of plurisubharmonic smooth local defining functions. Moreover, we give general criteria equivalent to the existence of plurisubharmonic smooth defining functions on or near the boundary of the domain. These equivalent characterizations are then explored for some classes of domains.
Cite
@article{arxiv.2204.13270,
title = {On plurisubharmonic defining functions for pseudoconvex domains in $\mathbb{C}^2$},
author = {Anne-Katrin Gallagher and Tobias Harz},
journal= {arXiv preprint arXiv:2204.13270},
year = {2022}
}
Comments
32 pgs., included a family of smoothly bounded, pseudoconvex domains which do not admit smooth local defining functions in Section 3; introduced the notion of sesquiconvexity, a new geometric notion sufficient for the existence of plurisubharmonic defining functions in Section 7